The SABR stochastic volatility model with β-volatility β є (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation between the stochastic differentials that appear on the right hand side of the model equations is considered. A series expansion of the transition probability density function of the mo...

or conclusions contained in this study should not be interpreted as representing the official opinion or policy of either ARPA or the USAF. DISTRIBUTION STATEMENT This documrnl lias hrun approved for puMic relrasr and sale; its distrihution is unlimited. This Rand Memorandum is presented as a competent treatment of the subject, worthy of publication. The Rand Corporation vouches for the quality...

Using the language of exponential Riordan arrays, we study three distinct families of orthogonal polynomials defined by trigonometric functions. We study the moment sequences of theses families, finding continued fraction expressions for their generating functions, and calculate the Hankel transforms of these moment sequences. Results related to the Euler or zigzag numbers, as well as the gener...